Example test routines (described, not code):

A test program for the ZX Spectrum is a specialized piece of software designed to check the integrity of the computer's hardware components. Unlike a video game, these utilities perform systematic checks on the system's Random Access Memory (RAM), Read-Only Memory (ROM), Central Processing Unit (CPU), Video Chip (ULA), keyboard, sound, and peripheral ports.

This is arguably the most famous and active open-source diagnostic tool. It supports a wide range of machines (16K to +3) and can be used with various ROM replacement devices.

23 Jun 2014 — Test Program (1985)(Sinclair Research) : Free Download, Borrow, and Streaming : Internet Archive. Internet Archive Test Program - World of Spectrum

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Use a mobile app like PlayZX or TAPir to convert the file into audio.